Phase Equilibria of the In–Pd–Sn System at 500 °C and 800 °C: Experimental Study and CALPHAD Modeling

Phase equilibria in the In–Pd–Sn system were investigated by a combination of key experiments and thermodynamic modeling. Partial isothermal sections at 500 °C and 800 °C of the In–Pd–Sn system for Pd contents above 66 at.% have been plotted experimentally using scanning electron microscopy with energy-dispersive X-ray spectroscopy (SEM/EDX) and X-ray diffraction (XRD). The solubility of the third component in binary compounds InPd3 and Pd3Sn was determined. The new ternary compound τ1 was found in Pd contents ranging from 20 to 25 at.% and at Sn contents varying from 5 to approximately 17 at.% Sn. This compound crystallizes in an Al3Ti-type tetragonal structure. Isostructural InPd2 and Pd2Sn phases from the In–Pd and Pd–Sn binary compositions form a continuous phase field in the ternary system at both temperatures. The temperatures of the solidus, liquidus, and phase transitions of the alloys along the Pd–In50Sn50 line were measured using DTA/DSC. Thermodynamic calculation of the In–Pd–Sn ternary system is performed using the CALPHAD method using the Thermo-Calc® software. The thermodynamic properties of the disordered fcc and liquid phases were described by the Redlich–Kister–Muggianu model. To describe intermetallic phases, namely, InPd3, Pd3Sn, τ1 and Pd2(InxSn1−x), a two-sublattice models was used. Thermodynamic description of the In–Pd–Sn system obtained in this study is in good agreement both with our results and the published experimental data


Introduction
Palladium-based alloys are widely used in chemical, microelectronics, medicine, and a number of other industries. Components of such alloys are often low-melting nontransition metals, which improve casting characteristics and may serve as strengtheners [1]. They also form numerous intermetallic compounds with palladium. These compounds have a few positive properties, for example, they can be used as highly efficient, selective, and stable catalysts [2,3]. On the other hand, their formation can cause undesirable effects. For example, when using lead-free solders containing indium and tin, the formation of intermetallics can seriously deteriorate the mechanical and conductive properties of the solder joints in printed circuit boards [4,5]. In both cases, information on the conditions of formation, stability, and structure of intermetallic compounds is required, which is obtained in studies of palladium and low-melting metals phase diagrams.
For thermodynamic modeling of the ternary system, reliable descriptions of binary limiting systems are necessary. In this study, critical analysis of the existing thermodynamic descriptions in the In-Pd and Pd-Sn system was performed. Special attention was paid not just to experimental results reproducibility, but to mutual consistency of models of isostructural phases and of Gibbs energies of pure components in all the systems. Based on that, the authors made the following conclusions: - The thermodynamic description of the In-Pd system [13] uses the up-to-date Gibbs energies of components [14] and reproduces well the results of experimental studies of phase equilibria and phase thermodynamic properties. This description can be accepted in this work without any changes. - The thermodynamic calculation of the In-Sn system was performed in three works [15][16][17]. The results in [15] are in the best agreement with the experimental data for phase equilibria. According to other studies, the γ phase present in the system turns out to be too stable, which is why its calculated homogeneity field is much wider than the experimental one. In all the In-Sn system calculations [15][16][17], obsolete values [18] of indium stability parameters in the β tin-type structure and of tin in the In type structure were used. The description of the In-Sn system requires revision. - The most complete thermodynamic description of the Pd-Sn system, taking into account the latest studies of phase equilibria in the system, was proposed in [19]. Two models for the liquid phase: the Redlich-Kister polynomial and the associated solution theory were used. Both provide essentially the same quality of the reproduction of all the experimental data available.
Thus, for thermodynamic modeling of the In-Pd-Sn ternary, additional experimental data are required after studying the phase equilibria in this system at palladium content above 60 at.%. In addition, the thermodynamic description of the In-Sn binary system should be revised.

Experimental Procedures
In total, 32 alloys weighing 1 g each were obtained to study phase equilibria in the In-Pd-Sn system. Powder palladium (99.95% wt.), tin wire (99.95% wt.), and indium bars (99.999% wt.) were used as source materials. The alloys were produced in a Buehler MAM 1 arc furnace in an ultra-pure argon (99.9999%) atmosphere purified by preliminary melting of a getter (hafnium). Afterwards, the samples were annealed in evacuated silica ampoules with subsequent quenching in cold water. The annealing times were chosen according to our experience with the similar systems. At 800 • C, the annealing time was 1680 h (14 samples), and at 500 • C for 3600 h (18 samples). The high content of palladium in the alloys and the previous studies of the authors of similar systems with palladium [20,21] were taken into account when choosing the annealing time.
The alloys obtained were examined by X-ray diffraction (XRD), scanning electron microscopy (SEM), energy-dispersive X-ray (EDX) analyses, and differential thermal analysis (DTA). XRD was performed by a DRON-4 diffractometer using monochromatized CuKα radiation (graphite monochromator in the secondary beam) and by STOE STADI P diffractometer, using monochromatized CuKα1 radiation (germanium monochromator). The obtained sets of reflections were indexed using the STOE Win XPOW (Ver. 2.24) software package.
Metallographic studies and EDX analysis were performed using Carl Zeiss LEO EVO 50XPV scanning electron microscope with an INCA Energy 450 energy dispersive analysis system (Oxford Instruments) operating at an accelerating voltage of 30 kV and a beam current of 30 µA. A Q-BSD detector was used to increase the image contrast. To determine the composition of the phase, the content of each element was determined at 3-5 randomly selected points belonging to the phase. The averages of the phase composition were taken from all the points. The composition of the alloy was determined in a similar way. The content of each component was measured in three randomly selected areas of the sample surface. The overall composition was taken as the average over three values.
The liquidus and solidus temperatures were determined by DTA, using STA 449 F1 Jupiter thermal analyzer (Netzsch, Germany). Runs were performed with a scanning rate 20 • C min −1 .

Thermodynamic Model
The thermodynamic description of In-Pd-Sn system was obtained following the CALPHAD approach. Here, each phase is assigned its own model according to the structure, composition and other factors. The Gibbs energy function of temperature and composition contains some parameters to be evaluated [22].
Thermo-Calc ® software (version 2021b) was used for calculations. The Gibbs energy functions of the phases of the pure components were extracted from PURE5 database provided with the Thermo-Calc ® software package [14].
The liquid (L) and fcc (α) disordered phases were described by the substitutional solution model where the Gibbs free energy G ψ is given as: where x i is mole fraction of a component i, and G ψ i is Gibbs energy of the component i in the structure of Ψ phase.
The excess Gibbs energy term Xs G ψ in (1) were modelled by the Redlich-Kister polynomial [22,23]: Here, L i,j coefficients are interaction parameters that are generally to be assessed.

Thermodynamic Models of Phases with Sublattices
To describe intermetallic phases, the conventional sublattice model [22] was taken. Here, the Gibbs energy of a phase with sublattices is expressed as: where ∆ 0 f G end is the Gibbs energy of the endmembers, a s is the stoichiometric coefficient of s sublattice, y s i is the site fraction of i species in s sublattice. The excess Gibbs free energy Xs G ψ includes the interaction parameters of the components in the sublattices, which can be optimized.
The parameters of the phase models were evaluated in two steps. Reasonable initial values were estimated by trial and error. Where possible, the values were refined through the PARROT module of the Thermo-Calc ® software (version 2022b).

Experimental Investigations
The results of XRD and EDX analyses of the samples at 500 and 800 • C are listed in Tables 2 and 3.   Palladium-rich areas of isothermal sections of the In-Pd-Sn system at 500 • C and 800 • C, built according to the data from Tables 2 and 3 At both temperatures, the α-solid solution boundary is determined basing on the results of the study of samples 1-3, 8 and 9 (Tables 1 and 2). It almost coincides with the line connecting the values of indium and tin solubility in palladium. Just as in both boundary systems, it almost does not change with the temperature.
The existence of continuous solubility between the phases InPd2 and Pd2Sn with orthorhombic structure of the Co2Si type at 500 °C was confirmed by studies of samples 10-18, whereas at 800 °C, by the studies of samples 10-14. The compositions of single-phase samples and tie-lines of two-phase equilibria at two temperatures are plotted on the isothermal triangles ( Figure 1) according to EDX data (Tables 2 and 3). The existence of continuous solubility between the phases InPd 2 and Pd 2 Sn with orthorhombic structure of the Co 2 Si type at 500 • C was confirmed by studies of samples 10-18, whereas at 800 • C, by the studies of samples 10-14. The compositions of singlephase samples and tie-lines of two-phase equilibria at two temperatures are plotted on the isothermal triangles ( Figure 1) according to EDX data (Tables 2 and 3).
Three phases are in equilibrium with the α-solid solution and the Pd 2 (In x Sn 1−x ) phase in the In-Pd-Sn system: a low-temperature modification of the InPd 3 compound with the Al 3 Zr-type crystal structure, τ 1 ternary phase with Al 3 Ti-type structure, and Pd 3 Sn-based solid solution with the AuCu 3 -type structure. Note that all the above structure types are derived from the Cu-type structure by ordering (AuCu 3 ) or ordering with simultaneous tetragonal lattice distortion (Al 3 Zr, Al 3 Ti).
Note that the crystal structures of both the InPd 3 and τ 1 phases as identified from the powder patterns appearing as disordered In-type structures. Since the atoms of indium, tin, and palladium have very similar values of atomic X-ray scattering factors [24], superstructure reflections intensity was essentially zero. For this reason, to determine the crystal structure of In-type tetragonal phases in samples 1-6, 8-11, and 13, we used an approach similar to that described in [20,21]. This approach is based on the results of [8,9,25], who found that in the In-Pd binary system, the low-temperature modification of InPd 3 (Al 3 Ti-structure) and the high-temperature modification of the InPd 3 compound (Al 3 Zr-structure) differ in the ratio of c/a parameters for their face-centered pseudocubic subcells. The c/a ratio equal to 0.935 corresponded to the Al 3 Zr-type structure, and the c/a equal to 0.91 corresponded to the Al 3 Ti-type structure. Figure 2 shows the dependence of the c/a values of tetragonal phases in Samples 1-6, 8-11 and 13 annealed at 800 • C on tin content. In the samples with a tin content of up to 5.5 at.% (samples No. 13 and 1), the c/a ratio varies from 0.93 to 0.945, and the remainder from 0.905 to 0.92. This indicates that at 800 • C and a content of Sn of up to~6%, the low-temperature modification of InPd 3 (Al 3 Zr-structure) exists, whereas at a content of Sn from~5 to~17 at.%, the τ 1 phase with the Al 3 Ti-type structure is stable. The minimum tin content in the τ 1 phase was determined by the study of sample 10, and the maximum one is determined by the composition of the τ 1 phase in the three-phased sample 9. BSE images and XRD patterns of Samples 1, 10, and 9 annealed at 800 • C are presented in Figure 3. determined by the composition of the τ1 phase in the three-phased sample 9. BSE images and XRD patterns of Samples 1, 10, and 9 annealed at 800 °C are presented in Figure 3.  The XRD data of Sample 1 at 800 °C (Table 2, Figure 3а) indicate the presence of an α-solid solution and two tetragonal phases with с/а values of 0.948 and 0.915. As noted above, the first one refers to the InPd3 compound, the second one refers to the τ1 phase. The EDX analysis did not determine the composition of the τ1 phase due to its very low The XRD data of Sample 1 at 800 • C (Table 2, Figure 3a) indicate the presence of an α-solid solution and two tetragonal phases with c/a values of 0.948 and 0.915. As noted above, the first one refers to the InPd 3 compound, the second one refers to the τ 1 phase. The EDX analysis did not determine the composition of the τ 1 phase due to its very low content in the sample; however, the α phase (In12.7Pd83.7Sn3.6) and InPd 3 (In17.0Pd77.5Sn5.5) uniquely determine one side of the tie triangle α + InPd 3 + τ 1 , as well as the tin solubility (~6 at.%) in the InPd 3 compound at 800 • C. On the contrary, the results of EDX and XRD for that sample annealed at 500 • C show a τ 1 phase composition with somewhat lower (~5 at.%) tin content. This suggests that when the temperature drops from 800 • C to 500 • C, tin solubility in InPd 3 decreases insignificantly.
The homogeneity field of the Pd 3 Sn phase at 800 • C was determined by the XRD method for the two-phased samples 6, 12, and 14 and the three-phased samples 8, 9, and 11 ( Table 2). The maximum solubility of indium in the Pd 3 Sn phase was determined in the study of Sample 11 s. According to the XRD, the sample relates to the three-phase equilibrium of Pd 2 (In x Sn 1−x ) + Pd 3 Sn + τ 1 (Figure 3d). However, EDX was unable to determine the composition of Pd 3 Sn. Therefore, the solubility of indium in the Pd 3 Sn phase was found from dependence of the lattice spacing of that phase on In content ( Figure 4). It is close to ∼10 at.%.

Differential Thermal Analysis
The results of the studies of isothermal sections were supplemented w mental data on temperatures of phase transitions of four alloys obtained using methods. Four samples annealed at 500 °C with compositions on a line conne palladium and the equiatomic composition of the In-Sn system were selected. from the two-phase region Pd2(InxSn1−x) + Pd20Sn13 was synthesized. The results study are presented in Table 4.
The solidus temperature was determined as the onset of the peak of melt heating curve. Obvious supercooling was observed during crystallization, so th temperature was determined as the last peak on the heating curve ( Figure 5). Th atures of all phase transitions on the samples studied are resumed in Table 4. Th and solidus temperatures were used in determining of phase models' p whereas temperatures of other phase transitions were used for validation of ca At 500 • C, the solubility of indium in Pd 3 Sn is less than 10 at.% since at such an indium content, not Pd 3 Sn, but the τ 1 phase of (In10.4Pd76.3Sn13.3) composition is formed (Table 3,  sample 6). Thus, the solubility of the third component in the Pd 3 Sn phase decreases to some extent, as in the InPd 3 phase.

Differential Thermal Analysis
The results of the studies of isothermal sections were supplemented with experimental data on temperatures of phase transitions of four alloys obtained using DTA/DSC methods. Four samples annealed at 500 • C with compositions on a line connecting pure palladium and the equiatomic composition of the In-Sn system were selected. Sample 19 from the two-phase region Pd 2 (In x Sn 1−x ) + Pd 20 Sn 13 was synthesized. The results of the DSC study are presented in Table 4. The solidus temperature was determined as the onset of the peak of melting on the heating curve. Obvious supercooling was observed during crystallization, so the liquidus temperature was determined as the last peak on the heating curve ( Figure 5). The temperatures of all phase transitions on the samples studied are resumed in Table 4. The liquidus and solidus temperatures were used in determining of phase models' parameters, whereas temperatures of other phase transitions were used for validation of calculations.

In-Sn System
As noted above, the thermodynamic calculation of the In-Sn system [15] is in good accordance with the experimental data on phase equilibria and phase thermodynamic properties. However, it used outdated Gibbs energy values for the tin in the In-type structure (TET_ALPHA1) and for indium in the β-Sn type structure (BCT_A5), so the available calculation for the In-Sn system had to be revised in this work. Taking into account the new values of stability parameters, _ and _ , a good agreement with the experiment was achieved by changing the parameters of the indium-tin interaction in these two phases, and the parameters of models of other phases were left unchanged. Optimization of the parameters of the β-phase and tin-based solid solution was performed using the PARROT module of Thermo-Calc software using as input experimental data on phase boundaries and coordinates of invariant equilibria [26][27][28][29]. Figure 6 shows the In-Sn system equilibrium diagram calculated using the parameters obtained. Heat curves for Samples 2 and 6 are shown in Figure 5a,b. Sample 2 started to melt at 1333 • C and ended at 1342 • C. In Sample 6, the heat curve showed that the effect at 619 • C corresponds to the τ 1 →(τ 1 + Pd 3 Sn) transition. This is confirmed by the fact that Sample 6 annealed at 800 • C contains the Pd 3 Sn compound in addition to the τ 1 phase ( Table 2). The melting starts at ∼1335 • C and ends at 1378 • C.

In-Sn System
As noted above, the thermodynamic calculation of the In-Sn system [15] is in good accordance with the experimental data on phase equilibria and phase thermodynamic properties. However, it used outdated Gibbs energy values for the tin in the In-type structure (TET_ALPHA1) and for indium in the β-Sn type structure (BCT_A5), so the available calculation for the In-Sn system had to be revised in this work. Taking into account the new values of stability parameters, G TET_ALPH A1 Sn and G BCT_A5 In , a good agreement with the experiment was achieved by changing the parameters of the indium-tin interaction in these two phases, and the parameters of models of other phases were left unchanged. Optimization of the parameters of the β-phase and tin-based solid solution was performed using the PARROT module of Thermo-Calc software using as input experimental data on phase boundaries and coordinates of invariant equilibria [26][27][28][29]. Figure 6 shows the In-Sn system equilibrium diagram calculated using the parameters obtained.

In-Sn System
As noted above, the thermodynamic calculation of the In-Sn system [15] is in good accordance with the experimental data on phase equilibria and phase thermodynamic properties. However, it used outdated Gibbs energy values for the tin in the In-type structure (TET_ALPHA1) and for indium in the β-Sn type structure (BCT_A5), so the available calculation for the In-Sn system had to be revised in this work. Taking into account the new values of stability parameters, _ and _ , a good agreement with the experiment was achieved by changing the parameters of the indium-tin interaction in these two phases, and the parameters of models of other phases were left unchanged. Optimization of the parameters of the β-phase and tin-based solid solution was performed using the PARROT module of Thermo-Calc software using as input experimental data on phase boundaries and coordinates of invariant equilibria [26][27][28][29]. Figure 6 shows the In-Sn system equilibrium diagram calculated using the parameters obtained.

In-Pd System
Since the ternary phase τ 1 found in the In-Pd-Sn is isostructural with the βInPd 3 phase of the In-Pd binary, we assumed that the addition of tin stabilizes the high-temperature modification of the InPd 3 compound, and the single model was used for both phases. For the β-InPd 3 phase [13] suggested a formal two-sublattice model (Pd) 0.74 (In) 0.26 which corresponds to the phase composition. However, in the ternary, palladium content in τ 1 phase varies from 74 at.% to 80 at.%. To account for these data, the β-InPd 3 phase model was expanded to (Pd) 0.74 (In,Pd) 0.26. The parameters G In:Pd and 0 L In,Pd:Pd were determined by optimization, which used the data for both In-Pd and In-Pd-Sn systems simultaneously. The parameters of models of all other phases of the In-Pd system remain unchanged. As a result, we managed to preserve and, in some cases, even improve the description of temperatures and compositions of invariant equilibria with participation of this phase in the In-Pd binary ( Table 5). The resulting parameters of the βInPd 3 phase model are listed in Table 6.

Pd-Sn System
For the Pd 2 Sn phase of the Pd-Sn system, a single-sublattice model (Pd 2 Sn) 1 was used [19], whereas a two-sublattice model (Pd) 0.667 (In) 0.333 was proposed in [13] for the InPd 2 phase of the In-Pd system. As these phases actually form continuous solid solution in the ternary, similar models should describe both. For this purpose, the model of the Pd 2 Sn phase in the Pd-Sn system was replaced by the (Pd) 0.667 (Sn) 0.333 one. The stability parameter of the single end-member Pd 2 Sn was determined as G Pd2Sn (Pd:Sn) = 1 /3G Pd2Sn Pd2Sn . The above-mentioned model of the βPd 3 In/τ 1 phase in the ternary transformation turns into the Pd 0.74 (In,Pd,Sn) 0.26 one. The Pd:Pd and Pd:In endmembers as well as the Pd:(In,Pd) interaction corresponding to the In-Pd binary. Their values were determined during the revision of its description.
The values of the Gibbs energy function of the Pd:Sn endmember and the interaction parameter Pd:(Pd,Sn) correspond to the virtual phase in the Pd-Sn edge. The phase with gross composition Pd 0.8 Sn 0.2 was found as metastable still in 1957 [31]. In the ternary, the τ 1 phase closely approaches that composition at both 500 and 800 • C. Moreover, no significant slope changes between the fcc/fcc + τ 1 and fcc/fcc + Pd 3 Sn boundaries were detected in the present work. This means that in the Pd-Sn binary, the stability (Gibbs energy) of the virtual τ 1 phase with the Al 3 Ti-type structure is close to the stability of the phase with a Cu 3 Au-type structure.
When the stable phase Pd 3 Sn is suspended for some reason, the "nearly stable" τ 1 phase should be in equilibrium with the fcc solid solution and the Pd 2 Sn compound. The coordinates of these metastable equilibria were estimated by extrapolation of experimental ternary equilibria towards the Pd-Sn side.
The difference between enthalpies of formation of Pd 3 Sn phases with Cu 3 Au and Al 3 Ti type structures was taken from the ab initio calculation presented in the OQMD [32]. Gibbs energy function of the virtual Pd:Sn end-member of the τ 1 phase was calculated by adding of this difference to the Gibbs energy function of stable Pd 3 Sn phase [19] Other parameters of the virtual τ 1 phase in the Pd-Sn binary were obtained from estimated metastable equilibria with its participation.

In-Pd-Sn Ternary System Modeling
The initial data for calculating the In-Pd-Sn ternary system were the enthalpy of mixing of liquid alloys [12], data on phase equilibria obtained in the present work and taken from [6], and the phase transition temperatures obtained in the present work. The optimization also used the liquidus temperatures determined by kinks (slope breaks) of dependence of mixing enthalpy on concentration at 900 • C [12].
The parameters of the model of phases in the In-Pd-Sn system were determined as follows. First, the parameters of the phase models of all the phases were determined basing on phase equilibria separately at each temperature of 500 • C, 700 • C, 800 • C, and 900 • C. The resulting values were approximated using the a + b·T function. After that, all parameters were jointly optimized in the PARROT module of the Thermo-Calc ® software package, taking into account all the above experimental data.
For each temperature, the parameters of the ternary interactions for α phase were determined, without which the stability of the phase would be too high, which, in turn, would significantly change the character of the calculated phase equilibria.
The next phase was the liquid. The authors of [12] noted that their experimental data on the enthalpies of mixing of liquid alloys are well described by the Toop model. However, its software support, for example in Thermo-Calc ® , is much weaker than that of more commonly used Muggianu model. Moreover, the latter was used in our previous calculations of related systems (f.e. [21]), and unification of models is highly desirable. In addition, the present authors tested [33] the performance of Toop and Muggianu models using the Ag-Au-In system as test case. With inclusion of proper ternary interactions both provided the results of nearly the same quality. For these reasons the parameters of the ternary interaction, in the first approximation, were chosen as follows. The excess Gibbs energies of melt were calculated in a dense grid of temperatures and compositions using Toop's model. Then, the resulting values were approximated using Muggianu's model with the ternary interaction parameters. The parameters, approximating the results of Toop calculation, were slightly changed in subsequent optimization. After obtaining the model parameters for the liquid and α phase, other phases were added sequentially: In 3 Pd, τ 1 , Pd 3 Sn, In 7 Pd 3 , PdSn 2 , Pd 2 (In x Sn 1−x ), Sn 20 In 13 , InPd and PdSn.
The resulting parameter values are presented in Table 6. Those called "estimated" were fixed on the values obtained at the first stage of calculations.
The calculated isothermal sections of the In-Pd-Sn ternary are shown in Figure 7. Good agreement between the calculation results using experimental data on phase equilibria [6] and the results of this study can be noted.
It should be noted that a three-phase triangle (InPd + PdSn + PdSn 2 ) is present on the isothermal section at 700 • C. However, the PdSn 2 phase in the Pd-Sn system is formed only at 600 • C. As noted by the authors [6], the three-phase samples were partially melted. It is likely that the composition attributed to the PdSn 2 phase actually corresponds to a crystallized melt. Figure 8 shows a comparison of the calculated and experimental polythermal section Pd-In 50 Sn 50 of the In-Pd-Sn ternary. Experimental data are presented as transition temperatures obtained in this work. Note that only the liquidus and solidus temperatures were used for the search of parameters of phase models. The good agreement between the calculated and experimental temperatures of other phase transitions confirms that the obtained description of the In-Pd-Sn ternary system is correct.

Figure 8.
Pd-In50Sn50 part of the In-Pd system polythermal section in comparison with the DTA results (crosses indicate DTA results; circles indicate data [12]). Figure 9 shows a comparison between the calculated and experimental mixing enthalpy models for the liquid phase [12]. It can be noted that there is an excellent agreement between them.  Figure 9 shows a comparison between the calculated and experimental mixing enthalpy models for the liquid phase [12]. It can be noted that there is an excellent agreement between them.

Conclusions
Isothermal sections in the palladium-rich region of the In-Pd-Sn ternary system at 500 °C and 800 °C were determined using SEM, EDX and XRD methods. A ternary compound τ1 isostructural with a high-temperature modification of the βInPd3 phase was found. The ternary compound exists in the range of 4 at% to 16.5 at% (at 500 °C) or 18 at.% Sn (at 800 °C). At the same time, the palladium content in this phase increases from ∼75 at.% to 80 at.%. Phase transition and melting temperatures in four samples were determined along the Pd-In50Sn50 section using DTA. Liquidus temperatures were used in determination of parameters of model of melt, and temperature of other phase transitions to confirm the correctness of calculations.
The CALPHAD calculation of the In-Pd-Sn ternary was performed. Good agreement between the calculated and experimental data was reached, both for the data obtained in

Conclusions
Isothermal sections in the palladium-rich region of the In-Pd-Sn ternary system at 500 • C and 800 • C were determined using SEM, EDX and XRD methods. A ternary compound τ 1 isostructural with a high-temperature modification of the βInPd 3 phase was found. The ternary compound exists in the range of 4 at% to 16.5 at% (at 500 • C) or 18 at.% Sn (at 800 • C). At the same time, the palladium content in this phase increases from~75 at.% to 80 at.%. Phase transition and melting temperatures in four samples were determined along the Pd-In50Sn50 section using DTA. Liquidus temperatures were used in determination of parameters of model of melt, and temperature of other phase transitions to confirm the correctness of calculations.
The CALPHAD calculation of the In-Pd-Sn ternary was performed. Good agreement between the calculated and experimental data was reached, both for the data obtained in the present work and for the published data for phase equilibria and for thermodynamic properties of the melt. In addition, good agreement of the calculated phase transition temperatures with experimental DTA data not used in the optimization confirms that the obtained description of the In-Pd-Sn system is correct.